The length of a rectangular garden is modeled by the expression x+2 and the width is modeled by the expression 2x-3. Write an expression for both perimeter and area of the rectangular garden in terms of x.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

It may help you to begin by drawing a picture to model this problem, labeling one side of the rectangle x+2 and the other side 2x-3 (although this step is not necessary).

1) Perimeter: The perimeter of a shape is the distance around the outside.  Generally you just add up the side lengths.  In the case of a rectangle, since the two lengths are the same and the two widths are the same, it can be shortened to the following formula:


All that needs to be done is to substitute the expressions given for length and width into the formula above:


Then you just need to simplify the expression on the right by distributing and combining like terms:



So the expression for the perimeter of the garden is 6x-2.


2) Area: The area of a shape is the amount of space inside of it (for which the formulas vary widely depending on the shape).  The formula for the area of a rectangle is


Once again, you just need to substitute the given expressions for length and width:


In order to simplify, you will need to distribute the binomials (often call the FOIL method) and combine like terms:



So this is the expression for the area of the garden.


See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial